findOptimalSmacofSym: Selecting the optimal multidimensional scaling (MDS)...

In mdsOpt: Searching for Optimal MDS Procedure for Metric and Interval-Valued Data

Selecting the optimal multidimensional scaling (MDS) procedure

Description

Selecting the optimal multidimensional scaling procedure - metric MDS (by varying all combinations of normalization methods, distance measures, and metric MDS models) and nonmetric MDS (by varying all combinations of normalization methods and distance measures)

Usage

findOptimalSmacofSym(table,
critical_stress=(max(as.numeric(gsub(",",".",table[,"STRESS 1"],fixed=TRUE)))+
min(as.numeric(gsub(",",".",table[,"STRESS 1"],fixed=TRUE))))/2,
critical_HHI=NA)

Arguments

table	result from optSmacofSym_nMDS or optSmacofSym_mMDS. Data frame ordered by increasing value of Stress-1 fit measure or HHI index with columns: Normalization method Distance measure MDS model Spline degree (valid only for optSmacofSym_mMDS results) STRESS 1 HHI spp
critical_stress	threshold value of Kruskal's Stress-1 fit measure. Default - mid-range of Kruskal's Stress-1 fit measures calculated for all MDS procedures
critical_HHI	threshold value of Hirschman-Herfindahl HHI index. Only one parameter critical_stress or critical_HHI can be set, and the function finds the optimal value among the procedures for which the selected measure is lower or equal treshold value

Value

Nr	number of row in table with optimal multidimensional scaling procedure
Normalization_method	normalization method used for optimal multidimensional scaling procedure
MDS_model	MDS model used for optimal multidimensional scaling procedure
Spline_degree	Additional spline.degree value for optimal procedure, if mspline model is used for simulation. For other models there is no value for this field
Distance_measure	distance measure used for optimal multidimensional scaling procedure
STRESS_1	value of Kruskal Stress-1 fit measure for optimal multidimensional scaling procedure
HHI_spp	Hirschman-Herfindahl HHI index, calculated based on stress per point, for optimal multidimensional scaling procedure

Author(s)

Marek Walesiak [e-mail], Andrzej Dudek [e-mail]

Department of Econometrics and Computer Science, Wroclaw University of Economics and Business, Poland http://keii.ue.wroc.pl/mdsOpt/

References

Borg, I., Groenen, P.J.F. (2005), Modern Multidimensional Scaling. Theory and Applications, 2nd Edition, Springer Science+Business Media, New York. ISBN: 978-0387-25150-9. Available at: https://link.springer.com/book/10.1007/0-387-28981-X.

Borg, I., Groenen, P.J.F., Mair, P. (2013), Applied Multidimensional Scaling, Springer, Heidelberg, New York, Dordrecht, London. Available at: doi: 10.1007/978-3-642-31848-1.

De Leeuw, J., Mair, P. (2015), Shepard Diagram, Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.

Dudek, A., Walesiak, M. (2020), The Choice of Variable Normalization Method in Cluster Analysis, pp. 325-340, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

Herfindahl, O.C. (1950), Concentration in the Steel Industry, Doctoral thesis, Columbia University.

Hirschman, A.O. (1964). The Paternity of an Index, The American Economic Review, Vol. 54, 761-762.

Walesiak, M. (2014), Przegląd formuł normalizacji wartości zmiennych oraz ich własności w statystycznej analizie wielowymiarowej [Data Normalization in Multivariate Data Analysis. An Overview and Properties], Przegląd Statystyczny, tom 61, z. 4, 363-372. Available at: http://keii.ue.wroc.pl/pracownicy/mw/2014_Walesiak_Przeglad_Statystyczny_z_4.pdf

Walesiak, M. (2016a), Wybór grup metod normalizacji wartości zmiennych w skalowaniu wielowymiarowym [The Choice of Groups of Variable Normalization Methods in Multidimensional Scaling], Przegląd Statystyczny, tom 63, z. 1, 7-18. Available at: http://keii.ue.wroc.pl/pracownicy/mw/2016_Walesiak_Przeglad_Statystyczny_z_1.pdf

Walesiak, M. (2016b), Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling, Ekonometria, 2(52), 9-21. Available at: doi: 10.15611/ekt.2016.2.01.

Walesiak, M., Dudek, A. (2017), Selecting the Optimal Multidimensional Scaling Procedure for Metric Data with R Environment, STATISTICS IN TRANSITION new series, September, Vol. 18, No. 3, pp. 521-540.

Walesiak, M., Dudek, A. (2020), Searching for an Optimal MDS Procedure for Metric and Interval-Valued Data using mdsOpt R package, pp. 307-324, [In:] K. S. Soliman (Ed.), Education Excellence and Innovation Management: A 2025 Vision to Sustain Economic Development during Global Challenges, Proceedings of the 35th International Business Information Management Association Conference (IBIMA), 1-2 April 2020, Seville, Spain. ISBN: 978-0-9998551-4-1.

See Also

data.Normalization, dist.GDM, dist, smacofSym

Examples

  
  library(mdsOpt)
  metnor<-c("n1","n2","n3","n5","n5a","n8","n9","n9a","n11","n12a")
  metscale<-c("ratio","interval")
  metdist<-c("euclidean","manhattan","maximum","seuclidean","GDM1")
  data(data_lower_silesian)
  res<-optSmacofSym_mMDS(data_lower_silesian,normalizations=metnor,
  distances=metdist,mdsmodels=metscale,outDec=".")
  print(findOptimalSmacofSym(res))
  

mdsOpt documentation built on June 26, 2022, 5:05 p.m.